Mapping Types and Functions

The video tutorial explains the concept of functions and relations, focusing on different types of mappings: one-to-one, one-to-many, many-to-one, and many-to-many. It clarifies which mappings qualify as functions and which do not, emphasizing that one-to-one and many-to-one mappings are functions, while one-to-many and many-to-many mappings are not.

What is the primary condition for a relation to be considered a function?

• Every element in the domain has one and only one image in the range.

• Every element in the domain has multiple images in the range.

• Every element in the range has multiple pre-images in the domain.

• Every element in the range has no pre-image in the domain.

In a one-to-one mapping, what is true about the elements in the domain and range?

• Each element in the domain maps to multiple elements in the range.

• Each element in the range is an image of multiple elements in the domain.

• Each element in the domain maps to exactly one element in the range.

• Each element in the range has no corresponding element in the domain.

Which type of mapping ensures that a relation is always a function?

• One-to-one

• Many-to-many

• None of the above

• One-to-many

In a one-to-one mapping, what happens if an element in the domain has no image in the range?

• The relation is still a function.

• The relation is not a function.

• The relation becomes many-to-one.

• The relation becomes one-to-many.

Why is a one-to-many mapping not considered a function?

• Because each element in the range has multiple pre-images.

• Because each element in the domain maps to multiple elements in the range.

• Because each element in the range maps to exactly one element in the domain.

• Because each element in the domain has no image in the range.

In a many-to-one mapping, what is true about the relation?

• It is not a function because multiple elements in the domain map to the same element in the range.

• It is a function because each element in the range maps to multiple elements in the domain.

• It is not a function because each element in the range has multiple pre-images.

• It is a function because each element in the domain has one and only one image in the range.

What is a key feature of a many-to-one mapping?

• Each element in the domain has no image in the range.

• Each element in the domain maps to multiple elements in the range.

• Each element in the range has no pre-image in the domain.

• Multiple elements in the domain map to the same element in the range.

Which mapping type allows multiple elements in the domain to share the same image in the range?

• One-to-one

• Many-to-many

• Many-to-one

• One-to-many

What is the characteristic of a many-to-many mapping?

• Each element in the domain maps to exactly one element in the range.

• Multiple elements in the domain map to multiple elements in the range.

• Each element in the range is an image of exactly one element in the domain.

• Each element in the domain has no image in the range.

Why is a many-to-many mapping not a function?

• Because multiple elements in the domain map to multiple elements in the range.

• Because each element in the domain has no image in the range.

• Because each element in the domain maps to exactly one element in the range.

• Because each element in the range is an image of exactly one element in the domain.